Transcription of 2010北海道大 - izumi-math.jp
1 "2010 #a 2 1C y=2x 2C y=2x-4ax+4a (1) 1C 2C l (2) 2 1C 2C l 2 0 11 s 2 1C l 01p , 2p y=2p0x1-p+2p y=2px-2p !!!!1 2C l 0q , 2q-4aq1+4a y=02q1-4a x-2q+4a !!!!2 1 2 >=2p-2q4a=-2p+-2q4a p,q p=1-a , q=1+a l y=2011-a x-201-1a p D=0 2 0 11 t 2 l =1C 0 10 , 0 2C 02a , -42a1+4a =+-42a4a2a =2011-a f0 1x=2x, g0 1x=2x-4ax+4a f-0 1p=g-q=2011-a p=1-a , q=1+a s 2 1.
2 =2 x y O1C2 Clpq 1C :f0 1x=2ax+bx+c 0a1'0 2C :g0 1x=2ax+dx+e 0a1'0 1C 2C l y=ax+b 1C l 2ax+0b1-ax+c-b=a201-x p 2ax+0b1-ax+c-b=2ax-2apx+2ap >=-ba-2ap=-cb2ap >=b-a 2ap 1=c+b 2ap 2 2C l 2ax+0d1-ax+e-b=a201-x q 2ax+0d1-ax+e-b=2ax-2aqx+2aq >=-da-2aq=-eb2aq >=d-a 2aq 3=e+b 2aq 4 1C 8 -b2a , 9--2b4ac4a 2C 8 -d2a , 9--2d4ae4a 2 ---2b4ac4a89--2d4ae4a--b2a8 9-d2a =+01+d b01-d b4a01-c e201-d b =+67-2a2a01+p q672a01-p q4a67a01+p q01-p q4a01-p q 018 1,2,3.
3 4 =+2a67-2a2a01+p q42a01+p q4a =a wx y Opqlm 2 l m l S m2 .1C 2C x 0 12 1C 2C x y 2x 2x-4ax+4a x=1 x=+p q2=+01-1a01+1a2=1 x y Op+p q2q 1C 2C 1C :f0 1x=2ax+bx+c 0a1'0 2C :g0 1x=2ax+dx+e 0a1'0 " y 2ax+bx+c=2ax+dx+e 0b1-d x=e-c x=-e c-b d 88 -b2a'-d2a b9'd =-01+b2aq01+b2ap-01-a2ap01-a2aq =a01+q p01-q p2a01-q p +p q2 w
